Stable adaptive neural network control
type: Item
instance of: scholarly article
zbMATH Open document ID: 1001.93002
publication date: 2002-02-06T00:00:00Z
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1702344
zbMATH Keywords: adaptive neural network control
zbMATH Keywords: Lyapunov function method
zbMATH Keywords: nonlinear dynamical systems
zbMATH Keywords: Brunovsky form
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: transient performance
zbMATH Keywords: radial basis function neural network
zbMATH Keywords: triangular systems
MaRDI profile type: Publication
author: Shuzhi Sam Ge
author: Chang Chieh Hang
author: Tong Heng Lee
author: T. Zhang
title: Stable adaptive neural network control
published in: The Kluwer International Series on Asian Studies in Computer and Information Science (ASIS)
review text: Recent years have seen a rapid development of adaptive neural network control techniques and their applications. The main objective of the book is to develop stable adaptive neural control strategies and to perform transient performance analysis on the resulting neural control systems analytically. In this sense Lyapunov stability techniques play a critical role. Besides, mainly a class of single input single output (SISO) nonlinear systems, which can be rendered to the Brunovsky form, is considered. The book starts with a brief introduction to adaptive control, neural network (NN) control and the possible instability mechanisms in adaptive neural control systems in Chapter 1. Then Chapter 2 gives the brief summary of basic mathematical tools needed in the book. The next chapter presents radial basis function (RBF) NNs, which the authors call linearly parametrized NNs, and multilayer NNs, which are called nonlinearly parametrized nets. Let us mention that such a classification is not precise. In Chapter 4 the regionally stable NN design is proposed for a nonlinear system in the Brunovsky controller form. In the next chapter the integral Lyapunov function is introduced for adaptive control in the case of SISO nonlinear systems as well as for many-inputs many-outputs (MIMO) nonlinear systems. In Chapter 6, adaptive NN control is investigated for a class of nonaffine nonlinear systems. In the last Chapter 7, triangular nonlinear systems are treated using quadratic Lyapunov functions. Finally, the conclusion is proposed on the methods used in the book with a sketch of further research directions in the future. NEWLINENEWLINENEWLINEThe book is written in a good mathematical way. But unfortunately simulations are performed only for examples that are, in a sense, academic rather than for real applications. Also, it is very positive to learn that the authors are aware of some shortcomings of the method used. Namely, concerning the Lyapunov function technique, they say: ``Fo…
reviewed by: Ladislav Andrey
description: scientific article; zbMATH DE number 1702344